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Physics
Problem
Which one of the following correctly expresses the impulse delivered by a time-dependent force
F
(
t
)
F(t)
F
(
t
)
acting from
t
=
t
1
t=t_1
t
=
t
1
to
t
=
t
2
t=t_2
t
=
t
2
? a)
F
(
t
1
+
t
2
2
)
(
t
2
−
t
1
)
F\!\left(\dfrac{t_1+t_2}{2}\right)(t_2-t_1)
F
(
2
t
1
+
t
2
)
(
t
2
−
t
1
)
b) The area under the
F
F
F
–
t
t
t
curve between
t
1
t_1
t
1
and
t
2
t_2
t
2
(i.e.
∫
t
1
t
2
F
(
t
)
d
t
\displaystyle \int_{t_1}^{t_2} F(t)\,dt
∫
t
1
t
2
F
(
t
)
d
t
) c)
m
v
1
+
v
2
2
m\,\dfrac{v_1+v_2}{2}
m
2
v
1
+
v
2
d)
m
v
2
m v_2
m
v
2
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